Butter one side of each of the pieces of bread. Evenly divide the cheese amongst 4 slices of the bread, on the un-buttered sides. Place all of the bread, buttered side down, on the grill and cover the grill. Grill the bread until the bottom is lightly marked with grill marks, and the cheese is melted. You may need to remove the plain pieces of bread first, and move the cheese covered pieces to the top grill rack and cover the grill for a couple of extra minutes, so that the cheese melts but the bottoms of the bread slices don’t burn.
Spread the mayonnaise evenly over the unbuttered sides of the 4 pieces of toast. On the melted cheese slices, layer the bacon, lettuce and tomatoes, and season with salt and pepper. Place the mayonnaise spread slices mayo-side down on the sandwiches, slice, and eat warm.
Should a grill not be available to you, just make this on the stovetop, in a griddle pan if you have one, in a regular old pan if you don’t. A panini press would also be an excellent thought.